Suppose X1,..., X, are n iid random variables from the cumulative distribution func- tion F(x). Let Y = X; for i = 1,..., n. We further know that X; and Yi have the Y; same distribution. For 0.5 < p < 1, define - = Spinf{x F(x) p}. Our interest is to estimate (p. Throughout this question, we assume that the probability density function f(x) of F(x) is continuous and positive for all x. Let and n n = 2n I(X x) + i=1 2n i=1 -I(Y x) 10 np = inf{x : n(x) p}. (a) Find the limiting distribution of ( n.p - 5p) and argue that its asymptotic p(1-p) {f(p)} variance is smaller than {() Hint: start with P((n,p - p) x). Without loss of generality, we assume that x 0.